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Numbers - LCM (Lowest Common Multiple) and HCF - (Highest Common Factor)

These terms are not actually that hard to understand Just learn these simple facts:

The Lowest Common Multiple (LCM) is the SMALLEST number that will DIVIDE BY ALL the numbers in question.

E.g. 3, 6, 9, 12, 15 are all multiples of 3. 5, 10, 15, 20, 25 are all multiples of 5.

The lowest number that is in both lists is 15, so 15 is the LCM of 3 and 5.

The Highest Common Factor (HCF) is the BIGGEST number that will DIVIDE INTO ALL the numbers in question.

E.g. 1, 2, 4, 8 are all factors of 8. 1, 2, 3, 4, 6, 12 are all factors of 12. The highest number that is in both lists is 4, so 4 is the HCF of 8 and 12.

1 - Multiples and LCM

  1. List the first ten multiples of 6, starting at 6.
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  2. List the first ten multiples of 5, starting at 5.
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  3. What is the LCM of 5 and 6?
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2 - Factors. HCF (Highest Common Factor)

  1. List all the factors of 30.
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  2. List all the factors of 48.
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  3. What is the HCF of 30 and 48?
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3 - Find the HCF (Highest Common Factor)

For each set of numbers find the HCF.
I tell you what, it's a lot easier to find the LCM or HCF once you've listed the multiples or factors. If you miss this out it'll all go horribly wrong!
  1. 40, 60
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  2. 10, 40, 60
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  3. 10, 24, 40, 60
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  4. 15, 45
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  5. 15, 30, 45
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  6. 15, 20, 30, 45
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  7. 32, 64
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  8. 32, 48, 64
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  9. 16, 32, 48, 64
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4 - Find the LCM (Lowest Common Multiple)

For each set of numbers find the LCM.

  1. 40, 60
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  2. 10, 40, 60
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  3. 10, 24, 40, 60
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  4. 15, 45
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  5. 15, 30, 45
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  6. 15, 20, 30, 45
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  7. 32, 64
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  8. 32, 48, 64
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  9. 16, 32, 64
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5 - Find the LCM (Lowest Common Multiple)

Laura, Rita and Alan regularly go swimming. Laura goes every 2 days, Rita goes every 3 days and Alan goes every 5 days. They all went swimming together on Friday 1st June. This is just an LCM type question. Can you see why?
  1. On what date will Laura and Rita next go swimming together?
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  2. On what date will Rita and Alan next go swimming together?
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  3. On what day of the week will all 3 next go swimming together?
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  4. Which of the 3 (if any) will go swimming on 15th June?
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